Vacuum quantum effect for curved boundaries in static Robertson--Walker spacetime

TL;DR

This paper investigates the vacuum energy-momentum tensor for a conformally coupled scalar field between curved boundaries in a static Robertson--Walker spacetime, using conformal relations to Rindler space to derive results.

Contribution

It provides a method to compute vacuum expectation values in curved Robertson--Walker spacetime via conformal transformation from Rindler space.

Findings

Explicit expressions for the energy-momentum tensor in the given setup.

Demonstration of the conformal relation's utility in curved spacetime quantum field theory.

Insights into boundary effects in curved cosmological models.

Abstract

The energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in $k=-1$ static Robertson--Walker spacetime is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. $k=-1$ Robertson--Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in Robertson--Walker space from the corresponding Rindler counterpart by the conformal transformation.